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Since the behavior of PEMFCs depends on both advection and diffusion; a suitable alternative to the Modelica Fluid library and the stream concept is necessary. The proposed solution uses a "mixing" scheme based on the exponential of the Peclet numbers for each transport process. Storage and transport processes are co-located in each subregion of a rectilinear grid-all in the same base model. The Onsager formulation is used; whereby the effort and flow rate are conjugates of the entropy flow rate associated with energy transfer.
The implementation is modular; it allows species to be enabled indendently for each region. In addition; the geometric axes may be independently enabled (up to 3D) and shearing (transverse momentum) may be optionally included. Chemical/electrochemical inteactions are communicated in a fully acausal manner through expandable connectors.
This paper focuses on the motivation; background; and approach. Future publications will describe the ongoing work to calibrate; validate; and utilize the model for particular case studies. The library is made available as open source.
Keywords: PEMFC; three dimensional; fluid dynamics; electrochemistry; heat transfer; advection; diffusion; momentum; Onsager
Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
[2] R. B. Bird; W. E. Stewart; and E. N. Lightfoot. Transport Phenomena. John Wiley & Sons; 2nd edition; 2002.
[3] W. Borutzky. Bond Graph Modelling of Engineering Systems: Theory; Applications and Software Support. Springer; 2011.
[4] K. A. Burke. Unitized regenerative fuel cell system development. NASA report TM—2003-212739; Glenn Research Center; Cleveland; OH; Dec. 2003.
[5] F. E. Cellier and J. Greifeneder. Modeling chemical reactions in modelica by use of chemo-bonds. In F. Casella; editor; Proc. 7th Int. Modelica Conf.; Como; Italy; Sep. 2009. Modelica Assoc.; Linköping University Electronic Press.
[6] E. L. . Cussler. Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press; 2nd edition; 1997.
[7] K. L. Davies and R. M. Moore. Object-oriented fuel cell model library. Electrochem. Soc. T.; 11(1):797–808; Oct. 2007.
[8] K. L. Davies and R. M. Moore. PEMFCSim: A fuel cell model library in Modelica. In 31st Fuel Cell Seminar & Exposition; San Antonio; TX; Oct. 2007.
[9] K. L. Davies; R. M. Moore; and G. Bender. Model library of polymer electrolyte membrane fuel cells for system hardware and control design. In F. Casella; editor; Proc. 7th Int. Modelica Conf.; Como; Italy; Sep. 2009. Modelica Assoc.; Linköping University Electronic Press.
[10] K. L. Davies and C. J. Paredis. Natural unit representation in Modelica. In Proc. 9th Int. Modelica Conf.; Munich; Germany; Sep. 2012 (submitted). Modelica Assoc.
[11] J. H. Dymond; K. N. Marsh; R. C. Wilhoit; and K. C. Wong. Virial Coefficients of Pure Gases. Numerical Data and Functional Relationships in Science and Technology. Springer-Verlag; 2002.
[12] Dynasim AB. Dymola: Dynamic Modeling Laboratory; Mar. 2010. Ver. 7.4.
[13] F. P. Incropera and D. P. DeWitt. Fundamentals of Heat and Mass Transfer. John Wiley & Sons; 5th edition; 2002.
[14] J. Larminie and A. Dicks. Fuel Cell Systems Explained. John Wiley & Sons; 2nd edition; 2003.
[15] C. Mattiussi. The finite volume; finite element; and finite difference methods as numerical methods for physical field problems. volume 113 of Advances in Imaging and Electron Physics; pages 1–146. Elsevier Academic Press; 2000.
[16] B. J. McBride; M. J. Zehe; and S. Gordon. NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA report TP—2002-211556; Glenn Research Center; Cleveland; OH; Sep. 2002.
[17] B. A. McCain; A. G. Stefanopoulou; and K. R. Butts. A study toward minimum spatial discretization of a fuel cell dynamics model. In Proc. Int. Mech. Eng. Congr. Exposition (IMECE2006); number IMECE2006-14509; Chicago; IL; Nov. 2006. ASME.
[18] D. A. McKay; W. T. Ott; and A. G. Stefanopoulou. Modeling; parameter identification; and validation of water dynamics for a fuel cell stack. In Conf. on Fuel Cell Science; Engineering and Technology; Orlando; FL; Nov. 2005.ASME. FUELCELL2005-81484.
[19] Modelica Association. Modelica Standard Library. http://www.modelica.org/libraries/Modelica; Dec. 2009. Ver.3.1.
[20] M. J. Moran and H. N. Shapiro. Fundamentals of Engineering Thermodynamics. John Wiley & Sons; 6th edition; 2008.
[21] R. D. Present. Kinetic Theory of Gases. McGraw-Hill; 1958.
[22] M. A. Rubio; A. Urquia; L. Gonzá¡lez; D. Guinea; and S. Dormido. FuelCellLib: A modelica library for modeling of fuel cells. In Proc. 4th Int. Modelica Conf.; Hamburg-Harburg; Germany; Mar. 2005. Modelica Association.
[23] M. A. Rubio; A. Urquiaa; and S. Dormidoa. Dynamic modelling of PEM fuel cells using the FuelCellLib Modelica library. Math. Comp. Model. Dyn.; 16(3):165–194; Jun. 2010. doi: 10.1080/13873954.2010.506758.
[24] A. Salogni and P. Colonna. Modeling of solid oxide fuel cells for dynamic simulations of integrated systems. Appl. Therm. Eng.; 30(5):464–477; 2010. doi: 10.1016/j.applthermaleng.2009.10.007.
[25] R. A. Svehla. Transport coefficients for the nasa lewis chemical equilibrium program. NASA Technical Memorandum NASA; Lewis Research Center; Cleveland; OH; Apr. 1995.
[26] U.S. Department of Energy. Hydrogen; fuel cells & infrastructure technologies program: Multiyear research; development and demonstration plan. Technical report; Energy Efficiency and Renewable Energy; Oct. 2007. Section 3.4: Fuel Cells.
[27] N. Wagner; W. Schnurnberger; B. Mueller; and M. Lang. Electrochemical impedance spectra of solid-oxide fuel cells and polymer membrane fuel cells. Electrochim. Acta; 43(24):3785–3793; 1998. doi: 10.1016/S0013-4686(98)00138-8.
[28] A. Z. Weber; R. M. Darling; and J. S. Newman. Modeling two-phase behavior in PEFCs. J. Electrochem. Soc.; 151(10):A1715–A1727; 2004. doi: 10.1149/1.1792891.
[29] K. W. Woo and S. I. Yeo. Dalton’s Law vs. Amagat’s Law for the mixture of real gases. SNU J. Educ. Res.; 5:127–134; 1995.